D.c.analog calculator for rapidly generating electric power system loadflow solutions

ABSTRACT

An analog loadflow calculator includes a modularized analog network simulator which includes modular circuits representative of power system buses, lines, generators and loads and interconnected to simulate the power system. The modular generator circuits, load circuits and line circuits provide currents to be summed at appropriate bus circuits. The simulator operates to force observance of current and voltage laws and to provide the bus voltage solution.

United States Patent 1191 Haley et al.

1451 Aug. 13, 1974 D.C. ANALOG CALCULATOR FOR RAPIDLY GENERATING ELECTRIC POWER SYSTEM LOADFLOW SOLUTIONS Inventors: Paul H. Haley, Pittsburgh, Pa.;

Mark K. Enns, Ann Arbor, Mich.

Assignee: Westinghouse Electric Corporation,

Pittsburgh, Pa.

Filed: May 19, 1972 Appl. No.: 255,111

1m. 01 G06g 7/62 Field of Search 235/15121, 150.5, 150. 235/1511, 184; 307/18, 19, 20, 24, 30, 31, 52, 62; 444/1; 340/1725 References Cited UNITED STATES PATENTS 9/1967 Kaufman et a1. 235/1505 X 6/1971 Brussolo 235/1505 7/1972 Mitsui et a1 235/184 X 10/1972 VanEssen 340/1725 10/1972 Cohn 235/184 X OTHER PUBLICATIONS Load Flows By Hybrid Computation For Power System Operations; M. Enns, T. C. Giras & N. R. Carlson; IEEE Transactions on Power Apparatus and Systems, Nov/Dec. 1971, pp.2540-2547.

Primary ExaminerMalcolm A. Morrison Assistant E.raminerEdward J. Wise Attorney, Agent, or FirmE. F. Possessky [57] ABSTRACT An analog ioadflow calculator includes a modularized analog network simulator which includes modular circuits representative of power system buses, lines, generators and loads and interconnected to simulate the power system. The modular generator circuits, load circuits and line circuits provide currents to be summed at appropriate bus circuits. The simulator operates to force observance of current and voltage laws and to provide the bus voltage solution.

6' Claims, 41 Drawing Figures NORTH 19 13 g envtsooxv so) -4 5* 0 25 LOAD 3 134 PHlLADELPHIA {20 L2! 12 I56 2 3 EHV 14 g as 1'? s- BUFFALO 26 LOAD i WASHINGTON r 22 WvlAM /96 WW2? WHEELlNG 9 WEST LOAD

PAIENIEDMIGWQH 3,829,669

sum -"01 III 23 NORTH EHV . I4 /38 L7 BUFFALO [25 *LOAD EHV g WASHINGTON 78 22 wiw 96 -23 WHEELING WEST- LOAD. FIcsI INJECTION CURRENT VALVES A *1 4 D/A 4O TRAN MIssIoN LINE OUTAGE SWITCHING i DIGITAL SIMULATOR 0 W W W L BUS VOLTAGE VALVES I-INES.BUSES GENERATION TRANSFORMERS I so r' I I I3 L EHV(5OOKV 3a) -4 5* 25 0A L 0 g 3 I34 PHILADELPHIA PAIENIEI AUG I 3mm SHEEI 02 0F 23 BUS F 308 I ,3IO 1 z INTEGRATOR 1, 5p

' 3l4 ADMITTANCE I LINE (p'q) [323 I ADMITTANCE LN YPI' LINE I -II i I I I a I I325 (324 3|8 FIGS )4 ADMITTANCE Y pn 1E" l/306 LLINE (p-nI LINE'OUTAGE SWITCHING I I 45 [I] I A00 ANALOG 4|0- DIGHAL D/A GENERATION EQ COMPUTER POWER wP A AND LINE VOLTAGE MODULES T [E] MODULES T sET POINTS I BUS vOLTAGEs ANO LINE CURRENT SOLUTION H64 60 P r Pps De K Ip TO BUS-P PAtsmwwmw 6.626.666

sum '0 HF 23 LINE T0 BUS 5 10 us 1 LINE 1 FROM 22 BUSES (TRANSFORMER) 2 5 7 9 7 LINE ' FROM 1/0 TO BUS 9 LOAD 26 FROM 1/ GENERATOR ANALOG FAULTING MODULES CIRCUITRY PANEL(MANUAL) 8 D ITAL CONTROL FIG.|OA

PATENIEI] we I 3I974 MET 5 BF 23 LINE OUTAGE SWITCHING A/D BUS vOLTAGE AND LINE CURRENT SOLUTIONS 4l3 4I2 4|l D/A ANALOG I ANALOG DIGITAL POWER DYNAMIC BUS ANALOG COMPUTER VOLTAGE GENERATOR LINE LOADS SET POINTS MODULES [1G] MODULES [IL] I [IT] SWING ANGLES [E] ROTATIONAL vELOCITIEs 4|4 D/A INFINITE BUS vOLTAGE 'gfifig SET POINTS INFINITE BUSES DCU'S FOR LOAD ADMITTANCE ADJUSTMENTS FIG. IO

LINE CURRENT AND 4m BUS vOLTAGE SOLUTIONS I {410 [4" D/A [16] Bus DIGITAL ANALO COMPUTER 4 LINE OUTAGE- 'M D LOADSG SWITCHING O x [1L] ANALOG k TIESAND INFINITE 40! BUSES FIG H DCUS LOAD ADMITTANCE ADJUSTMENT FAULTING FAULTING DEVICE PATENTEB ms: 3 m4 saw u? or 23 FAULTING DEVICE FAULTING DEVICE FAULTING DEVICE PATENTED AUG 1 31974 sum as m 23 FIG.B5A.

REAL BUS VOLT INPUT IMAGINARY BUS VOLT PAIENTEDAIIM awn SHEET V AL4 ALB ALII

PATENIEDAHR1319H 3.829.669

sum" 11 or 23 ALIS ALIB

FlG.i7C

TO 0 DISPLAY so 602 603 R p JMS 8 l 8 M 2 ms S V RESOLVER v I I Pe sue Efl SIN8- p X 8 15wr 6:3 I

+ cos P E, I I 1! alt) Li Pmmwmm 3.829.668

sum "12 ur 23 INTRONICS MULTIPLIER mmomcs MULTIPLIER PAIENTEII III; I 3 I974 SHEET "13 0F 23 PH I r I A 704 709 705 n KP? SIGNAL f} .I GENERATOR J L F TYPICAL LINE-BUS coNNE cTIoN 10- J LINE PO I W 01 BUSF '0 -o 0-BUSQ0f0 LINE b c I TYPICAL GEN-BUS CONNECTION RdK b c a M 1 GENERATOR o o- BUS I S|2 O5 clS TYPICAL LOAD-BUS CONNECTION LOAD 0/O-- BUS SM 08 O FIG. 20

' PAIENIED mm 3x974 sum 16 U 23 O/A INF. BUS VOLTAGES O/A IE I, M 7 GENERATOR SET POINTS MODELS LINE [16] [H3 OATA TR F "2500 SWITCHING A S Q LINE 983 LlNK A/D ANALOG SIMULATOR MODELS SOLUTION [E] 982 LOADVADMITT. LOAD SETTINGS MODELS- SYSTEM STUDY OPERATORS MODE FIG. 24 

1. A DC analog simulator for AC power networks cpmprising a plurality of bus DC circuits, generator DC circuits, load DC circuits and line DC circuits, said bus DC circuits including first and second circuits for generating respective output voltage phasor signals corresponding to first and second coordinate components of the voltages at the respective buses, said generator DC circuits including third and fourth circuits for generating respective output current phasor signals corresponding to first and second coordinate components of generation currents for the actual generators, said load DC circuits including fifth and sixth circuits for generating respective output current phasor signals corresponding to first and second coordinate components of bus to load currents for the actual loads, said line DC circuits including seventh and eighth circuits for generating respective output current phasor signals corresponding to first and second coordinate components of at least the equivalent series branch currents for the actual lines, and means for interconnecting the bus, generator, load and line DC circuits in a manner corresponding to bus, generator, load and line interconnections in the AC network.
 2. A DC analog simulator as set forth in claim 1 wherein said first and second, third and fourth, fifth and sixth and seventh and eighth circuits operate with output signals respectively representative of real and imaginary quantities.
 3. A DC analog simulator as set forth in claim 1 wherein said bus, generator, load and line DC circuits comprise modular DC circuits.
 4. A DC analog loadflow calculator for simulation of an AC network, said calculator including a plurality of bus DC circuits, generator DC circuits, load DC circuits, and line DC circuits interconnected to correspond to the AC network, said generator DC circuits including means for receiving generator power and voltage magnitude actual and constraint input signals, said load DC circuits including means for receiving load power actual and constraint input signals, each of said bus DC circuits including means for responding to generator, load, and line phasor input current signals and for generating an output bus voltage phasor signal, each of said generator DC circuits including means for responding to the difference between said actual and constraint generator power input signals and means for responding to the difference between said actual and constraint generator voltage magnitude input signals, and for generating an output generator current phasor signal, each of said load DC circuits including means for responding to the difference between said actual and constraint load power power signals and for generating an output load current phasor signal, each of said line DC circuIts including means for responding to the difference between applied bus voltage phasor signals and generating an output line phasor current signal in accordance with at least a representation of the equivalent series branch impedance.
 5. A DC loadflow calculator as set forth in claim 4 wherein said means for receiving actual and constraint generator signals, said means for receiving said actual and constraint load power signals, means for responding to generator, load and line phasor current signals, and means for responding to the difference between applied bus phasor voltages comprise amplifiers.
 6. A DC loadflow calculator as set forth in claim 4 wherein said bus, generator, load and line DC circuits comprise modular DC circuits. 